This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Here are the steps to solve the problem: Step 1: Organize the raw data. The marks obtained by 40 students are: 51, 46, 38, 68, 21, 51, 58, 64, 72, 33, 86, 48, 67, 93, 71, 63, 44, 50, 22, 91, 78, 66, 52, 81, 43, 64, 53, 82, 45, 58, 57, 72, 62, 77, 61, 74, 88, 35, 43, 56. Sorting the data in ascending order: 21, 22, 33, 35, 38, 43, 43, 44, 45, 46, 48, 50, 51, 51, 52, 53, 56, 57, 58, 58, 61, 62, 63, 64, 64, 66, 67, 68, 71, 72, 72, 74, 77, 78, 81, 82, 86, 88, 91, 93. a) Construct a frequency distribution table. Using class intervals of 20-29, 30-39, 40-49, etc.: | Class Interval | Frequency (f) | Cumulative Frequency (cf) | |:---------------|:--------------|:--------------------------| | 20-29 | 2 | 2 | | 30-39 | 3 | 5 | | 40-49 | 6 | 11 | | 50-59 | 9 | 20 | | 60-69 | 8 | 28 | | 70-79 | 6 | 34 | | 80-89 | 4 | 38 | | 90-99 | 2 | 40 | | Total | 40 | | b) Draw a cumulative frequency curve for the distribution. To draw the cumulative frequency curve (ogive), plot the cumulative frequency against the upper class boundaries. The upper class boundaries are 29.5, 39.5, 49.5, 5